%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV878-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:00:06 PM UTC 2026
% Result : Unsatisfiable 0.18s 3.71s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 44 ( 21 unt; 0 nHn; 27 RR)
% Number of literals : 81 ( 11 equ; 43 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 2 con; 0-4 aty)
% Number of variables : 74 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_inf__min_0,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Orderings_Olinorder(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X1) = c_Orderings_Oord__class_Omin(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__min_0) ).
cnf(cls_linorder__class_OMin__def__raw_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_Olinorder__class_OMin(X1) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__class_OMin__def__raw_0) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(cls_finite_0,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).
cnf(clsarity_fun__Finite__Set_Ofinite_Ofinite,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
cnf(cls_Suc__n__not__le__n_0,axiom,
~ c_lessequals(c_Suc(X1),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
cnf(cls_Max__ge_0,axiom,
( ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_in(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X2,hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__ge_0) ).
cnf(cls_fold1__singleton_0,axiom,
hAPP(c_Finite__Set_Ofold1(X1,X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).
cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
cnf(cls_rangeI_0,axiom,
c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rangeI_0) ).
cnf(cls_finite__imageI_0,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
cnf(c_0_12,plain,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Orderings_Olinorder(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X1) = c_Orderings_Oord__class_Omin(X1) ),
inference(fof_simplification,[status(thm)],[cls_inf__min_0]) ).
cnf(c_0_13,plain,
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_Olinorder__class_OMin(X1) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_linorder__class_OMin__def__raw_0]) ).
cnf(c_0_14,plain,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Orderings_Olinorder(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X1) = c_Orderings_Oord__class_Omin(X1) ),
c_0_12 ).
cnf(c_0_15,axiom,
class_Lattices_Olower__semilattice(tc_nat),
clsarity_nat__Lattices_Olower__semilattice ).
cnf(c_0_16,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder ).
cnf(c_0_17,plain,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| c_Finite__Set_Ofinite(X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_finite_0]) ).
cnf(c_0_18,plain,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clsarity_fun__Finite__Set_Ofinite_Ofinite]) ).
cnf(c_0_19,plain,
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_Olinorder__class_OMin(X1) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1) ),
c_0_13 ).
cnf(c_0_20,plain,
c_Orderings_Oord__class_Omin(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_21,plain,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| c_Finite__Set_Ofinite(X2,X1) ),
c_0_17 ).
cnf(c_0_22,plain,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2)) ),
c_0_18 ).
cnf(c_0_23,plain,
~ c_lessequals(c_Suc(X1),X1,tc_nat),
inference(fof_simplification,[status(thm)],[cls_Suc__n__not__le__n_0]) ).
cnf(c_0_24,plain,
( ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_in(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X2,hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3),X1) ),
inference(fof_simplification,[status(thm)],[cls_Max__ge_0]) ).
cnf(c_0_25,axiom,
hAPP(c_Finite__Set_Ofold1(X1,X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) = X3,
cls_fold1__singleton_0 ).
cnf(c_0_26,plain,
c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),tc_nat) = c_Finite__Set_Olinorder__class_OMin(tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16])]) ).
cnf(c_0_27,plain,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X3)
| c_Finite__Set_Ofinite(X1,tc_fun(X2,X3)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
clsarity_bool__Finite__Set_Ofinite_Ofinite ).
cnf(c_0_29,plain,
~ c_lessequals(c_Suc(X1),X1,tc_nat),
c_0_23 ).
cnf(c_0_30,plain,
( ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_in(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| c_lessequals(X2,hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3),X1) ),
c_0_24 ).
cnf(c_0_31,axiom,
c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4),
cls_rangeI_0 ).
cnf(c_0_32,plain,
hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| c_Finite__Set_Ofinite(X1,tc_fun(X2,tc_bool)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( ~ c_in(c_Suc(hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),X1)),X1,tc_nat)
| ~ c_Finite__Set_Ofinite(X1,tc_nat) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_16])]) ).
cnf(c_0_35,plain,
c_in(X1,c_Set_Oimage(c_Finite__Set_Olinorder__class_OMin(tc_nat),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[cls_finite__imageI_0]) ).
cnf(c_0_37,plain,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X3)
| c_Finite__Set_Ofinite(X1,tc_fun(tc_fun(X2,X3),tc_bool)) ),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_38,plain,
~ c_Finite__Set_Ofinite(c_Set_Oimage(c_Finite__Set_Olinorder__class_OMin(tc_nat),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,tc_nat),tc_nat),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4) ),
c_0_36 ).
cnf(c_0_40,plain,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| c_Finite__Set_Ofinite(X1,tc_fun(tc_fun(X2,tc_bool),tc_bool)) ),
inference(spm,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_41,plain,
~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
c_Finite__Set_Ofinite(X1,tc_fun(tc_fun(tc_bool,tc_bool),tc_bool)),
inference(spm,[status(thm)],[c_0_40,c_0_28]) ).
cnf(c_0_43,plain,
$false,
inference(spm,[status(thm)],[c_0_41,c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV878-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 09:29:51 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 Running first-order theorem proving
% 0.16/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/3.71 % Version: 3.5.1
% 0.18/3.71 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.18/3.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/3.71 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.18/3.71 % Starting new_bool_3 with 300s (1) cores
% 0.18/3.71 % Starting new_bool_1 with 300s (1) cores
% 0.18/3.71 % Starting sh5l with 300s (1) cores
% 0.18/3.71 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2814677 completed with status 0
% 0.18/3.71 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.18/3.71 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.18/3.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/3.71 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.18/3.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/3.71 % No SInE strategy applied
% 0.18/3.71 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.18/3.71 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/3.71 % Starting SubtermCWHack with 136s (1) cores
% 0.18/3.71 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.18/3.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 113s (1) cores
% 0.18/3.71 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 113s (1) cores
% 0.18/3.71 % Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 0.18/3.71 % SubtermCWHack with pid 2814687 completed with status 0
% 0.18/3.71 % Result found by SubtermCWHack
% 0.18/3.71 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.18/3.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/3.71 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.18/3.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/3.71 % No SInE strategy applied
% 0.18/3.71 % Search class: FGHSM-FSLM32-DFFFFFNN
% 0.18/3.71 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/3.71 % Starting SubtermCWHack with 136s (1) cores
% 0.18/3.71 % Preprocessing time : 0.014 s
% 0.18/3.71
% 0.18/3.71 % Proof found!
% 0.18/3.71 % SZS status Unsatisfiable
% 0.18/3.71 % SZS output start CNFRefutation
% See solution above
% 0.18/3.71 % Parsed axioms : 847
% 0.18/3.71 % Removed by relevancy pruning/SinE : 0
% 0.18/3.71 % Initial clauses : 847
% 0.18/3.71 % Removed in clause preprocessing : 0
% 0.18/3.71 % Initial clauses in saturation : 847
% 0.18/3.71 % Processed clauses : 15483
% 0.18/3.71 % ...of these trivial : 616
% 0.18/3.71 % ...subsumed : 12601
% 0.18/3.71 % ...remaining for further processing : 2266
% 0.18/3.71 % Other redundant clauses eliminated : 623
% 0.18/3.71 % Clauses deleted for lack of memory : 0
% 0.18/3.71 % Backward-subsumed : 102
% 0.18/3.71 % Backward-rewritten : 36
% 0.18/3.71 % Generated clauses : 116772
% 0.18/3.71 % ...of the previous two non-redundant : 94535
% 0.18/3.71 % ...aggressively subsumed : 0
% 0.18/3.71 % Contextual simplify-reflections : 17
% 0.18/3.71 % Paramodulations : 116103
% 0.18/3.71 % Factorizations : 32
% 0.18/3.71 % NegExts : 0
% 0.18/3.71 % Equation resolutions : 637
% 0.18/3.71 % Disequality decompositions : 0
% 0.18/3.71 % Total rewrite steps : 50010
% 0.18/3.71 % ...of those cached : 46377
% 0.18/3.71 % Propositional unsat checks : 0
% 0.18/3.71 % Propositional check models : 0
% 0.18/3.71 % Propositional check unsatisfiable : 0
% 0.18/3.71 % Propositional clauses : 0
% 0.18/3.71 % Propositional clauses after purity: 0
% 0.18/3.71 % Propositional unsat core size : 0
% 0.18/3.71 % Propositional preprocessing time : 0.000
% 0.18/3.71 % Propositional encoding time : 0.000
% 0.18/3.71 % Propositional solver time : 0.000
% 0.18/3.71 % Success case prop preproc time : 0.000
% 0.18/3.71 % Success case prop encoding time : 0.000
% 0.18/3.71 % Success case prop solver time : 0.000
% 0.18/3.71 % Current number of processed clauses : 2128
% 0.18/3.71 % Positive orientable unit clauses : 463
% 0.18/3.71 % Positive unorientable unit clauses: 23
% 0.18/3.71 % Negative unit clauses : 222
% 0.18/3.71 % Non-unit-clauses : 1420
% 0.18/3.71 % Current number of unprocessed clauses: 79264
% 0.18/3.71 % ...number of literals in the above : 211639
% 0.18/3.71 % Current number of archived formulas : 0
% 0.18/3.71 % Current number of archived clauses : 138
% 0.18/3.71 % Clause-clause subsumption calls (NU) : 313675
% 0.18/3.71 % Rec. Clause-clause subsumption calls : 239057
% 0.18/3.71 % Non-unit clause-clause subsumptions : 5891
% 0.18/3.71 % Unit Clause-clause subsumption calls : 22010
% 0.18/3.71 % Rewrite failures with RHS unbound : 173
% 0.18/3.71 % BW rewrite match attempts : 3745
% 0.18/3.71 % BW rewrite match successes : 174
% 0.18/3.71 % Condensation attempts : 0
% 0.18/3.71 % Condensation successes : 0
% 0.18/3.71 % Termbank termtop insertions : 1648355
% 0.18/3.71 % Search garbage collected termcells : 1532
% 0.18/3.71
% 0.18/3.71 % -------------------------------------------------
% 0.18/3.71 % User time : 2.764 s
% 0.18/3.71 % System time : 0.110 s
% 0.18/3.71 % Total time : 2.874 s
% 0.18/3.71 % Maximum resident set size: 5244 pages
% 0.18/3.71
% 0.18/3.71 % -------------------------------------------------
% 0.18/3.71 % User time : 14.689 s
% 0.18/3.71 % System time : 0.485 s
% 0.18/3.71 % Total time : 15.174 s
% 0.18/3.71 % Maximum resident set size: 5376 pages
% 0.18/3.71 % E exiting
%------------------------------------------------------------------------------